# Bogglers

By Scott Kim|Thursday, February 1, 2001

A Bevy of Boxes

Boxed in? This month's puzzles will have you thinking not only outside the box but also inside and all about the box. Put on your special, spatial thinking cap and get in touch with your cube roots.

No Matter How You Slice It

Slicing a cube can produce many different shapes, depending on the angle of the cut. Make a slice parallel to one of the cube's faces, for instance, and you get a square (example 5). Snip off a corner in just the right way, and you get an equilateral triangle (example 2). Which of the other shapes below can you create by slicing straight through a cube?

Shape, Rattle, and Roll

Each of the 16 forms above is made up of six same-sized cubes connected face to face. There are, however, only eight different objects: Every shape has an identical mate shown at a different angle. For instance, shape A can be rotated so that it matches shape G. Can you identify the other seven matched pairs? Beware: Cubes can be hidden behind other cubes. Some shapes have more than one potential match (B, for example, could match either H or J), but only one solution will give each shape a mate.Arthur C. Clarke's short story "The Sentinel," which inspired 2001, features an alien artifact shaped like a tetrahedron (a solid bounded by four triangles). In the movie, the artifact— the mysterious monolith— is a hexahedron (a solid bounded by six quadrilaterals).

Cubist Revival

1.  {TRICKY} Try to fold a 1-x-7-inch rectangle of paper to make a cube that measures 1 inch on each edge (see the illustration at right). Do not cut or tear the paper. Hint: Some of the cube's surfaces will be covered by more than one thickness of paper.

2.  {MEDIUM} Following the same rules, fold a 1-x-30-inch rectangle of paper to make a cube that measures 2 inches on each edge.

3.  {HARD} Now fold a 1-x-15-inch rectangle to make a cube that measures more than 1 inch on each edge.

Solution

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Got new solutions for the puzzle? Want to see other people's solutions? Talk to the puzzle master in his discussion forum at www.scottkim.com.